A positroid is a special case of a realizable matroid, that arose from the study of totally nonnegative part of the Grassmannian by Postnikov. Postnikov demonstrated that positroids are in bijection with certain interesting classes of combinatorial objects, such as Grassmann necklaces and decorated permutations. The bases of a positroid can be described directly in terms of the Grassmann necklace and decorated permutation. In this paper, we show that the rank of an arbitrary set in a positroid can be computed directly from the associated decorated permutation using non-crossing partitions.
@article{10_37236_8256,
author = {Robert Mcalmon and Suho Oh},
title = {The rank function of a positroid and non-crossing partitions},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8256},
zbl = {1431.05035},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8256/}
}
TY - JOUR
AU - Robert Mcalmon
AU - Suho Oh
TI - The rank function of a positroid and non-crossing partitions
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8256/
DO - 10.37236/8256
ID - 10_37236_8256
ER -
%0 Journal Article
%A Robert Mcalmon
%A Suho Oh
%T The rank function of a positroid and non-crossing partitions
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8256/
%R 10.37236/8256
%F 10_37236_8256
Robert Mcalmon; Suho Oh. The rank function of a positroid and non-crossing partitions. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8256
